Question: Simplify to lowest terms. $\dfrac{56}{80}$
Solution: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 56 and 80? $56 = 2\cdot2\cdot2\cdot7$ $80 = 2\cdot2\cdot2\cdot2\cdot5$ $\mbox{GCD}(56, 80) = 2\cdot2\cdot2 = 8$ $\dfrac{56}{80} = \dfrac{7 \cdot 8}{ 10\cdot 8}$ $\hphantom{\dfrac{56}{80}} = \dfrac{7}{10} \cdot \dfrac{8}{8}$ $\hphantom{\dfrac{56}{80}} = \dfrac{7}{10} \cdot 1$ $\hphantom{\dfrac{56}{80}} = \dfrac{7}{10}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{56}{80}= \dfrac{2\cdot28}{2\cdot40}= \dfrac{2\cdot 2\cdot14}{2\cdot 2\cdot20}= \dfrac{2\cdot 2\cdot 2\cdot7}{2\cdot 2\cdot 2\cdot10}= \dfrac{7}{10}$